Introduction

Islamic Geometric Ornaments in Istanbul

“Everything is arranged according to Number”- Plato (429–347 B.C.)

I have been interested in applications of mathematics, in particular geometry, in architecture and art for years. Most of my works with Maple, MuPAD, and later with Mathematica, always had something to do with mathematics and art. When I first time came to the Middle East I was stunned with the amount of geometric forms and ornaments present here. This was my first rendezvous with Islamic Art.

Abu Dhabi, in the United Arab Emirates, is the place where I have spent more than ten years. Although it is a very modern and extremely fast developing city, we still can find wonderful decorations that are definitely some of the best examples of Islamic ornaments one can find in our modern world. Since my first days in the Emirates I started collecting books and articles on Islamic art, and taking thousands of photographs of mosques and hundreds of other places. One day I found in a local bookshop a book on Islamic ornaments by Keith Critchlow (see [4]), and this was the moment when I started looking at Islamic ornaments, and ornaments in general, as geometric constructions. I started analyzing each example that I was able to find on Abu Dhabi streets. Hundreds of drawings and geometric constructions, developed using an excellent computer program The Geometer’s Sketchpad, started filling up my desk and a number of folders. I knew that one day I would have to sit and put, in writing, all my adventures with Islamic art, but then it was not the right time.

The next milestone in my discovery of Islamic art was the Sheikh Zayed Grand Mosque built in Abu Dhabi in 2007. The beautiful shape of its domes, blue tilings in the passage around the mosque, and geometric ornaments with 5 fold symmetry were for me a completely new experience in Islamic art.

A significant milestone in my discovery path in Islamic art was my trip to Turkey. After visiting the magnificent Suleymaniye Mosque on the Third Hill in Istanbul I knew that I was ready to start writing my book on geometric ornaments in Islamic art. However, the topic is huge and I probably I will never be able to cover all major examples and topics related to the geometric ornaments in Islamic art. Therefore, I decided to concentrate on selected examples from Istanbul and see how much I can tell about them. A more complete book about geometry of Islamic ornaments will probably have to wait a while.

Sheikh Zayed Mosque in Abu Dhabi

Fig. 1 The Sheikh Zayed Grand Mosque in Abu Dhabi.

(Arabic: مسجد الشيخ زايد) in Abu Dhabi is the largest mosque in the United Arab Emiratesand the third largest mosque in the world.  It is named after Sheikh Zayed bin Sultan Al Nahyan, the founder and the firstPresident of the United Arab Emirates, who is also buried next to the mosque (outer right side). The mosque has been opened for worship since Eid Al Adha in December 2007.

Constructions done with the help of a computer program can make our work much easier and we can store them ready for reusing many times later. However, there is no greater pleasure than developing these constructions by hand on large sheets of paper, finishing them with crayons and enjoying our work framed and hung on the wall. Therefore, if you have time and appropriate skills please do not ignore the traditional way of developing geometric ornaments.In this book I am going to show a number of geometric constructions of Islamic ornaments. Such constructions can be developed by drawing them by hand. However, this work can only be used once. Such drawings cannot be reused and every time when we start the same or similar ornament we have to draw it from scratch. Therefore, I decided to use a computer program for plane geometry. A few of them are available. One can use The Geometer’s Sketchpad, GeoGebra, Cabri or Cinderella, and one has to choose the tool that is the most suitable for him. My first choice was The Geometer’s Sketchpad, in short Sketchpad[1]. I have been using it for years for modeling Chinese lattices, gothic windows, kaleidoscopic images, and fractals. Therefore, all constructions presented in this book will be developed using the Sketchpad specific environment and tools. However, most of my constructions can be created in a few other geometry programs. A very good choice can be GeoGebra[2] where the number of tools is greater than in Sketchpad and the functionality is very similar.

Finally, I have to mention an important matter. Constructions of Islamic geometric ornaments presented in this book are not exactly the same as one can find in many other books on Islamic art. I present here my own point of view – it is how a person educated in geometry with experience in various forms of computer graphics sees them.


The Geometer’s Sketchpad is a commercial product developed by KCP Technologies. An evaluation version of the program can be downloaded from http://www.keypress.com/Sketchpad

GeoGebra is an impressive software for teaching mathematics. It contains a module for 2D geometry. Newer versions of GeoGebra contain also a 3D geometry module (version 5, currently in early beta stage) and a Computer Algebra System (starting from version 4).  The GeoGebra software is free and it can be downloaded from the the web site  http://www.geogebra.org/cms/ 

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